(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the absolute max and min values of f on the set D.

f(x,y)=4xy^3 - (x^2)(y^2) - xy^3

D is the closed triangular region in the xy-plane with vertices (0,0) (0,6) and (6,0).

3. The attempt at a solution

I found my two critical points to be (1,2) and (2,0). Then I tried to evaluate the boundary points:

1) 0<x<6, y=0

2) 0<y<6, x=0

3) (6-y, y) because the third boundary line is y= -x+6

I don't know how to solve for the last boundary line though. I plugged in x=6-y in the original equation, got the expression (2y^3)-(12y^2). Do I just plug in numbers now?

My book gets (2,4) for the absolute min, which is a point on this 3rd boundary line. I just don't see how to come up with the point, though.

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# Homework Help: Abs max/min

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